Problem: Divide. Write the quotient in lowest terms. $3\dfrac{3}{4} \div \dfrac5{7} = $
First, let's rewrite $3\dfrac3{4}$ as a fraction: $3\dfrac{3}{4} \div \dfrac5{7} =\dfrac{15}{4} \div \dfrac{5}{7}$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{5}7$ is $\dfrac7{5}$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{15}{4} \div \dfrac{5}7=\dfrac{15}{4}\times\dfrac7{5}$ $=\dfrac{15\times 7}{4\times 5}$ $=\dfrac{ \stackrel{3}{\cancel{15}} \times~ 7 }{ 4\times\underset{1}{\cancel{5}}} $ $=\dfrac{3\times 7}{4\times 1}$ $=\dfrac{21}{4}$ We could also write this as $5\dfrac1{4}$.